Enriched finite volume approximations of the plane-parallel flow at a small viscosity (Q785562)

The authors present a semi-analytic approach to suggest a novel improved numerical quality of the classical finite volume (cFV) method, applied to singularly perturbed nonlinear fluid equations. Using a singular perturbation analysis, the authors derive the so-called corrector which is an analytic approximation of the velocity vector field near the boundary. By embedding this corrector into the cFV schemes, enriched FV (eFV) schemes for the velocity and vorticity equations are constructed. It is verified numerically that the novel eFV schemes reduce significantly the computational error of cFV schemes, especially near the boundary, and consequently produce better approximations.